Geometric phase analysis for mask alignment

ABSTRACT

A method of measuring overlay error comprises forming a first mask having a first alignment array comprising a periodic pattern of first features having a first periodicity, forming a second mask having a second alignment array comprising a pattern of second features having the first periodicity, the first alignment array being adjacent the second alignment array, the first alignment array and the second alignment array forming a combined alignment array, transforming the combined alignment array to produce a transformed array, selecting a first region within the transformed array, inverse transforming the region to produce geometric phase shift information, averaging the phase shift information, converting the averaged phase shift information into a value for misalignment in a first direction corresponding to the first region, repeating the selecting, inverse transforming, averaging and converting using a second region within the transformed array to calculate a value for misalignment in a second direction corresponding to the second region, calculating an overlay error between the first and second mask levels by adding the components of misalignment in the first direction and second direction.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to methods for measuring themisalignment, or overlay error, between the patterns created on a waferin different steps of the integrated circuit manufacturing process, andmore specifically to improved methods of measuring misalignment whichutilize geometric phase analysis.

2. Description of the Related Art

During the process of integrated circuit fabrication, several hundredprocessing steps may be required as thin layers of semiconductors,insulators and metals are deposited and patterned. The patterns in eachlayer of the integrated circuit are created using the process oflithography. A photosensitive resist ("photoresist") is deposited on thesilicon wafer and exposed to light through a mask carrying the desiredpattern. The photoresist is then developed and removed from areascorresponding to the pattern, allowing the pattern to be transferred byetching into the layer below.

With every generation of smaller and faster integrated circuits, thesize of features in the masks is reduced, and the accuracy with whichfeatures in each layer must be aligned with those formed in previouslayers must increase. Therefore, the problem of measuring themisalignment between features formed in different layers has become morecritical. State of the art 64 Mb dynamic random access memory (DRAM)chips contain circuits with features as small as 250 nanometers (nm),and performance of the circuit is affected if one set of features ismisaligned by more than about 10 nm from the set of features formed inprevious processing steps. The placement precision, or cumulativedifference between patterns from various mask levels, is commonly called"overlay error".

To measure the amount of misalignment, or overlay error, the industrycurrently makes use of an alignment technique illustrated in FIGS. 1Aand 1B. Each mask includes several alignment areas, separate from thewiring or other pattern of the circuit. These alignment areas containalignment marks which are cross-shaped or chevron-shaped features,usually several microns in length. FIG. 1A shows a plan view of such analignment area.

The first alignment mark is etched onto the wafer at the first masklevel (referred to hereafter as level "A") and subsequent levels arealigned with respect to this mark. In the example illustrated here, thealignment mark for level "A" consists of four large chevrons (labeled"10" in FIG. 1A) arranged at the comers of a 50×50 micron square. Afterlevel "A" is patterned using the mask, the chevrons are easily visiblein an optical microscope. The next mask (referred to as level "B") isthen exposed. Level "B" has a smaller set of chevrons (labeled 11)which, if accurately aligned, will fit within the larger chevrons oflevel "A". After exposure and development of the photoresist for level"B", the alignment mark for level "B" is faintly visible in thephotoresist. By measuring the positions of the edges of the chevronsalong a line L-L', as shown in FIG. 1B, the degree of misalignment(labeled 12 in FIG. 1B) in the x direction can be measured. A similarmeasurement is then done in the y direction. If the error is beyondacceptable tolerances, the photoresist is washed off and the exposure ofthe level B mask is repeated.

This technique was originally developed for much larger feature sizes,but after several years of optimization this technique is now being usedto measure overlay error with an accuracy of 10 nm. This accuracy issufficient for present day needs but will be inadequate for futuregenerations of integrated circuits with smaller feature sizes requiringmore precise alignment. For these smaller circuits, yield problems occurwhen the conventional technique measures an acceptable overlay error andallows the wafer to be fully processed, but it is later found that thereis poor performance due to an overlay error smaller than can be resolvedusing the technique.

A separate problem of the conventional technique is that it relies onmeasurements of large alignment marks, several microns in size, whereasthe features in the actual circuits are much smaller, of the order of250 nm (or 0.25 microns). Large alignment marks are used because theyare visible in an optical microscope and therefore can easily bemeasured: the optical microscope can resolve features down to about 250nm. However, since the processing is optimized for the smaller featuresin the circuit, the edges of the large alignment marks may be improperlyetched, making it difficult to measure their positions. Moreimportantly, it may be difficult to relate the position of the largealignment marks to the positions of the small features in the actualcircuits, because large and small features are etched at different ratesduring processing.

To improve measurement accuracy, and to avoid the problems associatedwith using large alignment marks, several other overlay measurementtechniques have been suggested, such as techniques based on moirefringes. In moire fringe techniques, the alignment marks are large areasfilled with a regular pattern of small lines or dots.

In a typical example of a moire fringe technique, an alignment markconsisting of a regular pattern of dots is etched onto the wafer at thefirst mask level (again referred to as level "A"). The next mask level"B" is then exposed. The alignment mark for level "B" also consists of aregular pattern of dots and these are superimposed over the level "A"pattern. However, the level "B" pattern has a slightly different spacingbetween dots. Because of this difference in spacing, in some places the"A" and "B" dots are in registry, i.e. superimposed exactly, but inother places they are out of registry. Although individual dots are toosmall to see clearly in an optical microscope, the areas where dots arein and out of registry (the "moire fringes") can be distinguishedoptically. Visual inspection of the position of these areas is used todetermine the overlay error.

By using alignment marks which are made up of many small dots or lines,moire fringe techniques avoid the problems associated with using largefeatures for alignment marks. However, other significant problems occurwith moire fringe techniques. Three problems are worth noting. Firstly,once the level "A" pattern of dots is etched onto the wafer, it forms anon-planar surface on which the level "B" pattern must be placed. Thiscan distort the level "B" pattern and make it difficult to expose anddevelop correctly. A second problem is that the level "B" pattern showsvery weak contrast (since it is only patterned in photoresist) comparedto level "A" (which is etched onto the wafer). When superimposed ontothe high contrast level "A" pattern, level "B" is very difficult to see,making the moire fringes weak and the measurement less precise. A thirdproblem is that the difference in spacing between levels "A" and "B"must be small (around 1%) and carefully controlled in order to getappropriate moire fringes and this can be difficult to achieve.

The invention to be described below is significantly different from boththe moire and conventional techniques which have just been described, inthat it uses a different type of alignment mark combined withmathematical analysis to measure the overlay error. This enables theproblems described above to be avoided while also allowing an improvedaccuracy in the measurement of overlay error.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a structure and methodfor measuring the overlay error between at least two mask levels, eachof which includes specific alignment marks. These alignment marksconsist of repeating patterns of small dots or other features. All markshave the same spacing between features, and alignment marks fromsuccessive mask levels are placed next to each other. Mathematicalanalysis of the alignment marks is then used to calculate the overlayerror with a high degree of accuracy. For this, the invention makes useof mathematical techniques for the analysis of periodically repeatingpatterns, such as geometric phase analysis and other techniquesinvolving Fourier transforms.

More specifically, the invention comprises a method of measuring overlayerror comprising forming a first mask having a first alignment arraycomprising a periodic pattern of first features having a firstperiodicity, forming a second mask having a second alignment arraycomprising a pattern of second features having the first periodicity,the first alignment array being adjacent the second alignment array, thefirst alignment array and the second alignment array forming a combinedalignment array, transforming the combined alignment array to produce atransformed array, selecting a first region within the transformedarray, inverse transforming the region to produce geometric phase shiftinformation, averaging the phase shift information, converting theaveraged phase shift information into a value for misalignment in afirst direction corresponding to the first region, repeating the abovesteps using a second region within the transformed array to calculate avalue for misalignment in a second direction corresponding to the secondregion, calculating an overlay error between the first and second masklevels by adding the components of misalignment in the first directionand second direction. The transforming step comprises calculating aFourier transform and the inverse transforming step comprisescalculating an Inverse Fourier transform.

The invention can be used for accurate measurement of the overlay errorbetween mask layers during the fabrication of circuits with a smallfeature sizes of around 250 nm and below. The invention is significantlydifferent from, and has advantages over, both conventional and moiretechniques for overlay measurement. Overlay error is measured with anaccuracy of better than 2.5 nm, an improvement of at least four timesover the accuracy achieved using conventional techniques, and theinvention avoids the problems which have already been described forconventional and moire techniques.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects and advantages will be betterunderstood from the following detailed description of preferredembodiments of the invention with reference to the drawings, in which:

FIG. 1A is a schematic drawing of the alignment area used in aconventional technique for measuring overlay error in two directions;

FIG. 1B is a schematic drawing of a line scan made along line L-L' ofFIG. 1A, showing how overlay error is measured with the conventionaltechnique in one direction (the x direction);

FIG. 2A is a schematic drawing of the alignment area used in the presentinvention for measuring overlay error in two directions;

FIG. 2B is a schematic drawing of the alignment area used in aone-dimensional analog of FIG. 2A, to measure overlay error in onedirection;

FIG. 3 is a schematic drawing of a Power Spectrum of the alignment areaillustrated in FIG. 2A;

FIG. 4 is a schematic drawing of the Geometric Phase Map, or theimaginary part of the Inverse Fourier Transform, of the small region ofFIG. 3 enclosed by the circle;

FIG. 5 is a flow chart illustrating a preferred embodiment of theinvention; and

FIG. 6 is a schematic diagram of a computer system for implementing theinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

Referring now to the drawings, the inventive technique for themeasurement of overlay error using geometric phase analysis isillustrated. The discussion of the invention begins by describing thealignment marks which are used in this technique, and then describesmathematical calculations, using the technique of geometric phaseanalysis, with which the overlay error can be measured from thesealignment marks.

FIG. 2A shows the alignment marks used in the present technique, whichconsist of regular arrays of small dots or other features. The alignmentmarks are formed in an alignment area which is separate from the wiringpattern area of the masks.

At the first mask level, referred to hereafter as level "A", analignment mark (labeled 20 in FIG. 2A) is etched into the wafer. In apreferred embodiment, this alignment mark comprises an array of 10×20small dots, each dot being 550 nm across with a spacing between dots of550 nm. Therefore, in the example illustrated, the level "A" arrayoccupies an area of 11×22 microns.

The next mask level "B" is then exposed onto photoresist on the wafer.The alignment mark for level "B" is labeled 21 in FIG. 2A and isintentionally shown slightly misaligned. It can be seen that, unlike themoire fringe technique discussed above, the arrays for levels "A" and"B" have the same periodicity as each other, and are placed next to eachother rather than superimposed. The result is a "combined alignmentarray" which in this case is a square of size 22×22 microns.

The invention measures the misalignment between the two halves of thecombined alignment array. To measure the misalignment, the inventionanalyses the difference in position, or "geometric phase difference",between dots in the two arrays. In the preferred embodiment of theinvention, a series of calculations requiring the mathematical techniqueof Fourier Transforming is performed to determine the geometric phasedifference. The difference in position is analyzed separately in twodirections to give the misalignment in two directions. The preferredembodiment uses the x and y directions although any two differentdirections can be chosen.

The technique is best understood by reference to a simpler example givenin FIG. 2B. FIG. 2B represents a one-dimensional version of thetechnique, where misalignment must be measured in only one direction. Byfirst describing in general terms how the invention works in thisone-dimensional example, it will be easier to explain how thecalculation is done in the two-dimensional array shown in FIG. 2A.

The measurement required is the overlay error, labeled 22, between thetwo rows of dots 23 and 24 which correspond to levels "A" and "B"respectively. The relationship between the alignment marks and thepattern of wiring on the level "A" and "B" masks is chosen so that ifthe overlay error 22 is zero, the level "A" and "B" wiring in thecircuit will be perfectly aligned. Because of irregularities in thepositions of individual dots, it is inaccurate simply to measure thespacing between the closest dots in the two rows 23 and 24. Instead, aperfectly periodic curve 25 (here we use a sinusoidal curve) is fittedover the left hand row 23, using mathematical techniques to be describedbelow, and separately a sinusoidal curve 26 of identical periodicity isfitted over the right hand side 24. By fitting these curves over everydot in rows 23 and 24, inaccuracies in the positions of individual dotsare averaged out, improving the overall measurement accuracy. When curve25 is extended over the right hand side, it can be seen that because ofthe misalignment there is a lateral displacement, labeled 27, betweencurves 25 and 26. This lateral displacement, or "geometric phasedifference", can be calculated using Fourier transform techniques whichwill be described below.

The result of the calculation is expressed in degrees (where, forexample, a geometric phase difference of zero degrees means that thearrays are perfectly aligned and a geometric phase difference of 180°means that the arrays are exactly out of phase). The final stage of thecalculation is therefore to convert the geometric phase differenceexpressed in degrees into an overlay error expressed in nm by using thefact that a phase difference of 360° is equivalent to a displacement ofone dot spacing, labeled 28 in FIG. 2B (1100 nm in this case).

Note that this technique is unable to measure an overlay error greaterthan the spacing between dots, since for example an overlay error ofexactly one dot spacing will give a geometric phase difference of zero.In practice, this is not likely to be a problem since state of the artlithography tools can align successive masks to much better than the dotspacings which might be chosen. However, the technique can be combinedwith a conventional chevron technique to measure gross misalignment ifnecessary.

The measurement of overlay error in two dimensions, is discussed belowwith reference to the combined alignment array shown in FIG. 2A. Thecombined alignment array on the wafer is photographed, digitized andinput into a computer. In a preferred embodiment of the invention theresult is a stored image of dimensions 1024×1024 pixels, where the valueof each pixel is determined by the brightness of the corresponding areaof the original photograph.

A series of mathematical operations involving Fourier transformation,shifting and averaging is now performed on the stored image. All theoperations to be described can be carried out using a personal computerrunning a commonly available image processing package, such as the imageprocessing package available from Digital Micrograph, Pleasanton,Calif., U.S.A. Although each step is described individually and indetail below, the total computational time required is small, of theorder of a few seconds. In a preferred embodiment of the invention,these steps would be automated to minimize the total time required perwafer.

To begin the analysis, the Fourier Transform of the stored image of thecombined alignment array is calculated. The Fourier Transform is also atwo dimensional image, and, like the image of the combined alignmentarray, it may be stored digitally in the computer and displayed on acathode ray tube (CRT) display.

As would be known by one ordinarily skilled in the art given in thisdisclosure, the Fourier Transform is calculated using the equation

    G(u,v)=∫F(x,y)e.sup.-2 πi(ux+vy) dxdy.

Here F(x,y) is the value of the pixel at position (x,y) in the combinedalignment array, and G(u,v) is the value of the pixel at position (u,v)in the Fourier Transform of the combined alignment array. From thisequation it can be seen that the pixels G(u,v) in the Fourier Transformwill be complex numbers (even though the pixels in the combinedalignment array have real values). Note that the whole of the combinedalignment array, i.e. both halves of the image, are transformed togetherin this operation.

FIG. 3 illustrates the results of the calculation. Rather than showingthe Fourier Transform directly, FIG. 3 instead shows the Power Spectrumwhich is calculated simply by squaring the modulus of the FourierTransform. The Power Spectrum is shown because it illustrates theimportant features of the Fourier Transform, but is easier to depictbecause its pixels have real values rather than complex values.

It can be seen that the Fourier Transform consists of a pattern of peakshaving high intensity values, surrounded by a background of low or zerointensities. Each peak is made up of a group of 3×3 or more brightpixels and the peaks are arranged regularly throughout the FourierTransform.

The Fourier Transform is now manipulated mathematically to determine theoverlay error. Before describing how this can be done, we consider howthe information about the overlay error is represented in the FourierTransform.

As would be known by one ordinarily skilled in the art given in thisdisclosure, any image, such as the array in FIG. 2A, can be thought ofas being made up by superimposing a large number of regular sinusoidalwaves, much as the irregular surface of the ocean is determined by thesuperposition of many regular ocean waves. Each wave goes in a differentdirection and has a different amplitude (height), frequency (orwavelength) and phase. The Fourier Transform of any image is a recipe oringredient list showing which amplitudes, frequencies, phases anddirections are present in that image. The horizontal and verticaldirections in "transform space", i.e. u and v in FIG. 3, represent thefrequencies of waves going in the x and y directions in "real space",and the value of each pixel in the Fourier Transform G(u,v) gives thephase and amplitude of the wave with frequency (u,v).

The bright peaks in FIG. 3 therefore represent frequencies which appearstrongly in FIG. 2A. For example, the peak labeled 30 in FIG. 3represents a sinusoidal wave going horizontally (in the x direction)whose wavelength is equal to the spacing between dots in FIG. 2A: thiswave (the "fundamental frequency") is obviously an important componentof the image in FIG. 2A and therefore has a large amplitude in FIG. 3.The peak labeled 31 is another horizontal wave but with double thefrequency, or half the wavelength; it can be thought of as a "secondharmonic" and also appears strongly in FIG. 2A. Peak 32 is the thirdharmonic in the x direction, while peak 33 is the fundamental frequencyin the y direction. The dark areas represent frequencies which are notpresent in FIG. 2A.

All the information in FIG. 2A (including of course the relationshipbetween both halves of the pattern) is also stored in FIG. 3, and eachpart of FIG. 3 carries a particular portion of the information. Twoaspects of the information are important for the measurement of overlayerror using Fourier Transform techniques:

The information about the amount of misalignment in the x and ydirections is carried in the value of G(u,v) at the two fundamentalfrequencies 30, 33. To understand why this is so, suppose that themisalignment in say the x direction were zero. FIG. 2A would beperfectly periodic in the x direction (apart from random errors in theposition of each dot) and a single frequency and phase in peak 30 of theFourier Transform "recipe" would be sufficient to specify every dotposition in the x direction. If misalignment is present, a frequencywhich matches one side of FIG. 2A would be out of phase with the otherside; a second wave with the same frequency but with a different phasewould be required in the Fourier Transform. Both waves will contributeto the value of the Fourier Transform at the fundamental frequency.

Furthermore, the spatial information (i.e. that the right hand side ofthe image has one value of phase, and the left hand side has a secondvalue) is carried in the pixels immediately adjacent to the fundamentalfrequency. This group of satellite pixels making up peak 30 comprise an"envelope function" surrounding the fundamental frequency. As is knownto those skilled in the art, the nature of this group of satellite wavesis related to the spatial extent of the two regions with different phasein the original image.

Thus to determine the overlay error in the x direction, the value of theFourier Transform at the exact position of the fundamental frequency inpeak 30 must be analyzed to measure the phases of both components of thefundamental frequency, while the spatial information in the envelopefunction must be retained so that the phases of the two halves of thealignment array can be distinguished. In a preferred embodiment, this isdone in the following way:

Firstly, the center of peak 30 is determined by fitting a Gaussian curveto the peak, using processes well known to those ordinarily skilled inthe art. It is important to find the fundamental frequency exactly (tosub-pixel accuracy), but the width of peak 30 can make it difficult tomeasure the center of the peak accurately. However, as will be shownbelow, any errors in measuring the fundamental frequency can becompensated for later.

Secondly, the information from peak 30 is separated from the rest of theinformation in the Fourier Transform. This is done by drawing a circlearound the peak with an appropriate radius (in this example, a radius of3.5 pixels is large enough to include the pixels in the envelopefunction while excluding pixels from neighboring peaks such as 31 inFIG. 3), setting the value of every pixel outside this circle to zero("masking"), and then shifting the peak to the center (or origin) of theFourier Transform.

Thirdly, the masked and shifted peak 30 is converted back into an imagein real space by calculating an Inverse Fourier Transform. As is knownby those skilled in the art of Fourier analysis, the result of thisoperation is an image whose value at every point gives the phase andamplitude of the fundamental wave at that particular position in theoriginal image (of the combined alignment array). The Inverse Transformis calculated using the equation

    F'(x,y)=(.sup.1 /.sub.2 π)∫G'(u,v)e.sup.2 πi(ux+vy) du dv.

Here G'(u,v) is the value of the pixel at position (u,v) in the maskedand shifted Fourier Transform of the combined alignment array, andF'(x,y) is the value of the pixel at position (x,y) in the InverseTransform. Pixels in both G'(u,v) and F'(x,y) will have complex values.

Fourthly, the phase information is separated from the amplitudeinformation in the Inverse Transform by calculating the imaginary partof the Inverse Transform. FIG. 4 illustrates the result of thiscalculation. Each pixel in this image gives the value of the phase ofthe fundamental wave at that particular position in the originalalignment array. This type of phase information is referred to by thoseordinarily skilled in the art as a "geometric phase map". In thisexample it shows clearly a difference in the phase of the fundamentalwave between the left and right hand sides of the image. Irregularitiesin the positions of individual dots account for the fluctuations in thephase.

Fifthly, the phase difference between the two sides is calculated. Thevalues of pixels within two areas on either side, labeled 40 and 41 inFIG. 4, are averaged. These areas are chosen to avoid computationaleffects arising from proximity to the edge of the image. The average ofarea 40 is subtracted from the average of area 41. The difference isconverted into an average displacement (in terms of nanometers) byutilizing the mathematical principle that a phase difference of 360°corresponds to an image shift of one dot spacing.

The importance of determining exactly the frequency of the fundamentalwave was emphasized previously. The geometric phase map in FIG. 4provides a convenient way for testing whether the correct value of thefundamental frequency was determined. Suppose that an error occurs infinding the fundamental frequency in the first step, so that instead ofbeing shifted to the origin the fundamental frequency is only shifted todistance d from the origin. As is known to those skilled in the art,once the above calculations are performed, this error would result in afactor -2 πdx being added to the geometric phase map. It would look asif a uniform ramp or slope were added to the geometric phase map, makingit change gradually from bright to dark on each side instead of taking aconstant value on one side and a different but also constant value onthe other side. By looking at a part of the geometric phase map in whichthe average phase should be constant, such as area 40 in FIG. 4, thepresence of any such ramp can be detected and subtracted from the wholegeometric phase map before averaging areas 40 and 41.

Finally, a second similar analysis is done on spot 33 in FIG. 3 todetermine overlay error in the y direction.

The above process is illustrated in FIG. 5. More specifically, FIG. 5illustrates a method of measuring overlay error comprising forming afirst mask having a first alignment array comprising a periodic patternof first features 50, forming a second mask having a second alignmentarray comprising a pattern of second features having the sameperiodicity as the first alignment array 51, the first alignment arraybeing adjacent the second alignment array, the first alignment array andthe second alignment array forming a combined alignment array. Theprocess also includes transforming the combined alignment array toproduce a transformed array 52, selecting a first region within thetransformed array 53, inverse transforming the region to producegeometric phase shift information 54, averaging the phase shiftinformation 55, converting the averaged phase shift information into avalue for misalignment in a first direction corresponding to the firstregion 56, repeating the above steps using a second region within thetransformed array to calculate a value for misalignment in a seconddirection corresponding to the second region 57 and calculating anoverlay error between the first and second mask levels by adding thecomponents of misalignment in the first direction and second direction58.

The method described above was tested to determine the accuracy ofmeasurements made using the technique. The overlay error in testpatterns was calculated to within 2 nm, and testing also showed that itis possible to increase the accuracy further by digitizing with smallerpixel sizes. Thus with dedicated hardware allowing finer digitization,the resolution can be further increased.

A representative hardware environment for practicing the presentinvention is depicted in FIG. 6, which illustrates the typical hardwareconfiguration of an information handling/computer system in accordancewith the subject invention having at least one processor or centralprocessing unit (CPU) 60. CPUs 60 are interconnected via system bus 61to a random access memory (RAM) 63, read-only memory (ROM) 64,input/output (I/O) adapter 65 for connecting peripheral devices such asdisk units 65 and tape drives 67 to bus 61, user interface adapter 68for connecting keyboard 69, mouse 70, speaker 71, measurement tool 72,and/or other user interface devices such as touch screen device (notshown) to bus 61, communication adapter 73 for connecting theinformation handling system to a data processing network and/or alithography system 74, and display adapter 75 for connecting bus 61 todisplay device 76.

In a preferred embodiment of the invention a charge coupled device (CCD)camera is added directly to the optical microscope in a conventionaloverlay measurement tool. This enables a digital CCD image of thecombined alignment array to be recorded and sent directly to a computer,avoiding the steps described above of photographing the wafer anddigitizing the result and thereby speeding up the operation of theinvention. An array size of 1024×1024 was used in the analysis describedhere, but with a 2048×2048 CCD, which is commercially available frommany manufacturers, such as Gatan, Inc., Pleasanton, Calif., U.S.A.,digitization can be carried out at twice the spatial resolution, therebydoubling the accuracy.

The inventive arrays can be placed within the conventional alignmentmarks discussed above with respect to FIG. 1A. The area required (22×22microns) will fit within the 50 micron square used in the conventionaltechnique. The conventional technique may then be used to check forgross overlay error while the present technique gives a refined value.

This invention presents several advantages over conventional and moirealignment techniques. Compared to conventional techniques, the accuracyis higher; furthermore, the patterns used are those for which thelithography is optimized. Compared to moire techniques, there is no needto fabricate arrays with precise differences in spacing. Since thearrays are not superimposed, the alignment mark on the second level,which has low contrast because it is only patterned in photoresist, canbe distinguished more easily. Unlike moire techniques, the method caneasily be extended to allow multiple layers to be aligned. Since thealignment arrays are not superimposed, several layers can be aligned,each with respect to the previous one, by patterning arrays of dots nearto each other.

A specific advantage of the present technique is that information iscollected over a large area so the algorithm is insensitive to positionerrors in individual features of the array. Also, even though smallfeatures are used in the alignment marks, an optical microscope(connected to either a camera or a CCD) can be used to acquire the imageused in the analysis. This is because it is not necessary to resolve theexact shape of each dot precisely: since only the lowest (fundamental)frequencies are used in the analysis, the shapes of individual dots donot influence the results and dots which are close to the resolutionlimit of the optical microscope can be used. This is convenient becausethe feature sizes used in future generations of circuits are close tothe resolution limit (about 250 nm) of the optical microscope. Finally,there is no need for the two alignment arrays to contain identicalpatterns, so long as their periodicity is identical, so the techniquecan be applied using different patterns on each mask level if desired.

The benefits seen from this invention will primarily be related to theimproved yield which will become possible in the fabrication ofintegrated circuits with small feature sizes. However, geometric phaseanalysis is sensitive to defects and distortions in any regular array,and not just in an alignment array. The actual working elements of theDRAM structure comprise such a regular array, and so the invention canalso be useful in detecting small distortions and defects in the workingelement of circuits such as DRAMs.

While the invention has been described in terms of preferredembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theappended claims.

What is claimed is:
 1. A system for measuring overlay error comprising:afirst masking unit forming a first mask having a first alignment arraycomprising a periodic pattern of first features having a firstperiodicity; a second masking unit forming a second mask having a secondalignment array comprising a pattern of second features having saidfirst periodicity, said first alignment array being adjacent said secondalignment array; a digitizing unit digitally combining said firstalignment array and said second alignment array into a combinedalignment array; and a mathematical unit analyzing positions of saidfirst features and said second features in said combined alignment arrayto produce an overlay error between the first and second mask levels. 2.The system in claim 1, wherein said mathematical unit comprises:atransformer transforming said combined alignment array to produce atransformed array; a selector selecting a region within said transformedarray; an inverse transformer inverse transforming said region toproduce geometric phase shift information; and a converter convertingsaid phase shift information into a value for misalignment in adirection corresponding to said region.
 3. The system in claim 2,further comprising:a repetition unit repeating said selecting, inversetransforming and converting using a second region within saidtransformed array to calculate a value for misalignment in a seconddirection corresponding to said second region; and a second mathematicalunit calculating said overlay error between the first and second masklevels by adding the components of misalignment in said first directionand second direction.
 4. The system in claim 2, further comprising, asecond mathematical unit averaging said phase shift information.
 5. Thesystem in claim 2, wherein said transformer comprises a Fouriertransformer and said inverse transformer comprises an Inverse Fouriertransformer.
 6. A computer program product comprising a program storagedevice readable by a computer system tangibly embodying a program ofinstructions executed by said computer system to perform a process formeasuring overlay error, said process comprising:forming a first maskhaving a first alignment array comprising a periodic pattern of firstfeatures having a first periodicity; forming a second mask having asecond alignment array comprising a pattern of second features havingsaid first periodicity, said first alignment array being adjacent saidsecond alignment array; digitally combining said first alignment arrayand said second alignment array into a combined alignment array;andmathematically analyzing positions of said first features and saidsecond features in said combined alignment array to produce an overlayerror between the first and second mask levels.
 7. The computer programproduct in claim 6, wherein said mathematical analyzingcomprises:transforming said combined alignment array to produce atransformed array; selecting a region within said transformed array;inverse transforming said region to produce geometric phase shiftinformation; and converting said phase shift information into a valuefor misalignment in a direction corresponding to said region.
 8. Thecomputer program product in claim 7, further comprising:repeating saidselecting, inverse transforming and converting using a second regionwithin said transformed array to calculate a value for misalignment in asecond direction corresponding to said second region; calculating saidoverlay error between the first and second mask levels by adding thecomponents of misalignment in said first direction and second direction.9. The computer program product in claim 7, further comprising, aftersaid inverse transforming, averaging said phase shift information. 10.The computer program product in claim 7, wherein said transformingcomprises calculating a Fourier transform and said inverse transformingcomprises calculating an Inverse Fourier transform.